Question

A) Complete the table to find the product of (5y^2 - 6y) (7y^7 - y^3). Provide your answer in descending order of exponents. (2 points)

5y^2

-6y

Π

7y^7

Π

-у^3

(5y^2 - 6y) (7y^7 - у³) = _____

Answer 1

To find the product of the two polynomials \((5y^2 - 6y)(7y^7 - y^3)\), we can use the distributive property (also known as the FOIL method for binomials). We will multiply each term in the first polynomial by each term in the second polynomial.

Let's break it down:

1. **Multiply \(5y^2\) by each term in \(7y^7 - y^3\)**:
- \(5y^2 \cdot 7y^7 = 35y^{9}\)
- \(5y^2 \cdot (-y^3) = -5y^{5}\)

2. **Multiply \(-6y\) by each term in \(7y^7 - y^3\)**:
- \(-6y \cdot 7y^7 = -42y^{8}\)
- \(-6y \cdot (-y^3) = 6y^{4}\)

Now, we compile all these products together:
- From \(5y^2\): \(35y^{9} - 5y^{5}\)
- From \(-6y\): \(-42y^{8} + 6y^{4}\)

Now, combining all these together:
\[
(5y^2 - 6y)(7y^7 - y^3) = 35y^9 - 42y^8 - 5y^5 + 6y^4
\]

Now, organize the terms in descending order of the exponents:
\[
= 35y^9 - 42y^8 - 5y^5 + 6y^4
\]

So, the completed product is:
\[
(5y^2 - 6y)(7y^7 - y^3) = 35y^9 - 42y^8 - 5y^5 + 6y^4
\]